DSE Statistical Inference and Hypothesis Testing 4

Question 1

Which nonparametric test is the rank-based alternative to the independent samples t-test?

Accepted Answer

Mann-Whitney U test

Answer

The Mann-Whitney U test compares rank sums from two independent groups without assuming normality, serving as an alternative to the two-sample t-test.

Question 2

In a two-sided hypothesis test with α = 0.05, the critical region is placed:

Accepted Answer

Split equally between both tails

Answer

A two-sided test splits α/2 = 0.025 into each tail, rejecting H₀ when the test statistic is extreme in either direction.

Question 3

What is a sufficient statistic?

Accepted Answer

A statistic that captures all the information in the data about the parameter of interest

Answer

A sufficient statistic T(X) for parameter θ means the conditional distribution of the data given T does not depend on θ, so T contains all parameter information.

Question 4

The Neyman-Pearson lemma states that the most powerful test for simple H₀ vs. simple H₁ uses:

Accepted Answer

A likelihood ratio threshold as the rejection region

Answer

Neyman-Pearson shows that rejecting H₀ when the likelihood ratio L(θ₁)/L(θ₀) exceeds a constant k produces the most powerful level-α test.

Question 5

A researcher tests 20 independent null hypotheses, each at α = 0.05. The expected number of false rejections under all null hypotheses being true is:

Accepted Answer

1

Answer

Expected false positives = 20 × 0.05 = 1, illustrating the multiple testing problem even when every null is actually true.

DSE - Data Science Practice Test

DSE - Data Science Practice Test

DSE Statistical Inference and Hypothesis Testing 4